B1;1609;0c Math 5: The Mathematics of Music and Sound, Dartmouth College, FALL 2010

Math 5: The Mathematics of Music and Sound - FALL 2010

Alex Barnett. Kemeny room 206, tel 6-3178, email:

eigenmode of a string (picture credit: Van Kooten)

Music and math have gone hand in hand for thousands of years. Come and explore the myriad mathematical connections underlying the workings of musical instruments, the human voice, hearing, acoustics, sound analysis, musical composition, and more.

Sound and music are integral parts of all cultures and are critical to human and animal communications. The production, transmission, and perception of sound is woven through with mathematics. With the goal of expanding both scientific and artistic horizons (and teaching you some ear-opening practical skills) we explore vibration, resonance, waves, musical instruments, the human ear, speech, architectural acoustics, harmony and dissonance, tuning systems, and composition.

Prerequisites: high-school algebra, trigonometry, and physics. Familiarity with musical notation or some instrument will help.

Fall 2008 Math 5 site: check out their projects and aural postings!

Student Final Projects

Variety of common Helmholtz resonators

Unusual soprano formant spectrogram
Here are the write-ups and some of the slides from the Fall 2010 projects. Enjoy!

Lectures / OH: Steele 008, MWF 10:00-11:05am (period "10"), important to attend since we'll do lots of demonstrations and group worksheets. X-hour is 12:00-12:50pm Thurs, and I will use intermittently for: review, problem-solving sessions, catch-up lectures, etc. Do not schedule anything regular in this X-hr. I encourage you to come to office hours, Monday 3-4pm, Tuesday 4-6pm.

Book(s): There are no required books, since students have found the lectures materials sufficient. However, if you want a reasonably-priced relevant book I suggest: Musimathics, Volume 1, by Gareth Loy (Published by MIT Press, reprinted and corrected edition, 2008). If you accidentally get the 2006 edition, you'll need the errata. This will be on reserve at Baker-Berry library; also see here for other useful books.

Homework: 8 weekly HW's due each Wednesday at start of lecture. I strongly encourage you to collaborate, and to try at least some of the relevant homework problems before the next lecture (leaving it all for Tuesday night risks you getting left behind in this fast-paced course.) Please make your working/reasoning as clear as you can, write clearly, don't be scared of using lots of space on the page, and staple your work. Late homework will not be accepted (unless by prior arrangement for a valid, and exceptional, reason). Your lowest HW score will be dropped.

Exams/Quizzes: There will be a couple of 20-minute in-class quizzes, 1 midterm, and 1 final. These will test both mathematical and conceptual understanding, and problem-solving. I will try to give you ample time to complete exam questions. However, the only key is to practise, practise, practise!

Project work: Project work (the last 2 weeks) is an important and fun part of this course (see info.) Examples: instrument or room acoustic analysis, inventing and building a new instrument, essay on history of music technology or composition, testing the human ear. It includes a brief presentation to the rest of class. You may work in groups up to 2 (since it's a small class this year). There will be a presentation day (which the last class really enjoyed doing) on

Aural postings: I want you to post interesting sounds, discuss real-world examples relevant to our course, articles, links, pictures, etc. on the Aural Postings page each week. This is a way for you to share phenomena/ideas/sounds you discover. We will discuss them each Monday.

Grades: Will be based on roughly, HW 20%, Quizzes 10%, Midterm 20%, Project & Aural postings 20%, Final exam 30%. Note the HW is not heavily weighted but is the main chance you get to practise solving problems and get feedback, so stay on top of it. Grades in Math 5 are not curved; other students' good performance will not hurt your grade. (So please work together and help each other out!)

Tutoring: Also, private tutoring through the College is possible; if a student receives financial aid, the College will pay for three hours of tutoring per week. If you would like to have such a tutor, please go to 301 Collis and apply as early as possible. For more information check here

Honor principle. Exams: no help given or received. Homework: group discussion and collaboration on HW is great and helpful. However, write-ups must be done individually (ie no copying).

Special needs: I encourage students with disabilities, including "invisible" disabilities like chronic diseases and learning disabilities, to discuss with us any appropriate accommodations that might be helpful. Let me know asap, certainly in first 2 weeks. Also stop by the Academic Skills Center in 301 Collis to register for support services.

Religious observance: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.